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Giulia Sacca : Intermediate Jacobians and hyperKahler manifolds

In recent years, there have been more and more connections between cubic 4folds and hyperkahler manifolds. The first instance of this was noticed by Beauville-Donagi, who showed that the Fano varieties of lines on a cubic 4folds X is holomorphic symplectic. This talk aims to describe another instance of this phenomenon, which is carried out in joint work with R. Laza and C. Voisin: given a general cubic 4fold X, Donagi and Markman showed in 1995 that the family of intermediate Jacobians of smooth hyperplane sections of X has a holomorphic symplectic form. I will present a proof of this conjecture, which uses relative compactified Prym varieties.

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